View source: R/family.extremes.R

cens.gumbel | R Documentation |

Maximum likelihood estimation of the 2-parameter Gumbel distribution when there are censored observations. A matrix response is not allowed.

```
cens.gumbel(llocation = "identitylink", lscale = "loglink",
iscale = NULL, mean = TRUE, percentiles = NULL,
zero = "scale")
```

`llocation, lscale` |
Character.
Parameter link functions for the location and
(positive) |

`iscale` |
Numeric and positive.
Initial value for |

`mean` |
Logical. Return the mean? If |

`percentiles` |
Numeric with values between 0 and 100.
If |

`zero` |
An integer-valued vector specifying which linear/additive
predictors are modelled as intercepts only. The value
(possibly values) must be from the set {1,2} corresponding
respectively to |

This VGAM family function is like `gumbel`

but handles observations that are left-censored (so that
the true value would be less than the observed value) else
right-censored (so that the true value would be greater than
the observed value). To indicate which type of censoring,
input
`extra = list(leftcensored = vec1, rightcensored = vec2)`

where `vec1`

and `vec2`

are logical vectors
the same length as the response.
If the two components of this list are missing then the
logical values are taken to be `FALSE`

. The fitted
object has these two components stored in the `extra`

slot.

An object of class `"vglmff"`

(see
`vglmff-class`

). The object is used by modelling
functions such as `vglm`

and `vgam`

.

Numerical problems may occur if the amount of censoring is excessive.

See `gumbel`

for details about the Gumbel
distribution. The initial values are based on assuming all
uncensored observations, therefore could be improved upon.

T. W. Yee

Coles, S. (2001).
*An Introduction to Statistical Modeling of Extreme Values*.
London: Springer-Verlag.

`gumbel`

,
`gumbelff`

,
`rgumbel`

,
`guplot`

,
`gev`

,
`venice`

.

```
# Example 1
ystar <- venice[["r1"]] # Use the first order statistic as the response
nn <- length(ystar)
L <- runif(nn, 100, 104) # Lower censoring points
U <- runif(nn, 130, 135) # Upper censoring points
y <- pmax(L, ystar) # Left censored
y <- pmin(U, y) # Right censored
extra <- list(leftcensored = ystar < L, rightcensored = ystar > U)
fit <- vglm(y ~ scale(year), data = venice, trace = TRUE, extra = extra,
fam = cens.gumbel(mean = FALSE, perc = c(5, 25, 50, 75, 95)))
coef(fit, matrix = TRUE)
head(fitted(fit))
fit@extra
# Example 2: simulated data
nn <- 1000
ystar <- rgumbel(nn, loc = 1, scale = exp(0.5)) # The uncensored data
L <- runif(nn, -1, 1) # Lower censoring points
U <- runif(nn, 2, 5) # Upper censoring points
y <- pmax(L, ystar) # Left censored
y <- pmin(U, y) # Right censored
## Not run: par(mfrow = c(1, 2)); hist(ystar); hist(y);
extra <- list(leftcensored = ystar < L, rightcensored = ystar > U)
fit <- vglm(y ~ 1, trace = TRUE, extra = extra, fam = cens.gumbel)
coef(fit, matrix = TRUE)
```

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